Joint moments of discounted compound renewal sums

Ghislain Léveillé and Franck Adékambi

Scandinavian Actuarial Journal, 2012, vol. 2012, issue 1, 40-55

Abstract: The first two moments and the covariance of the aggregate discounted claims have been found for a stochastic interest rate, from which the inflation rate has been subtracted, and for a claims number process that is an ordinary or a delayed renewal process. Hereafter we extend the preceding results by presenting recursive formulas for the joint moments of this risk process, for a constant interest rate, and non-recursive formulas for higher joint moments when the interest rate is stochastic. Examples are given for exponential claims inter-arrival times and for the Ho-Lee-Merton interest rate model.

Date: 2012
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DOI: 10.1080/03461238.2010.503426

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